ODE No. 1055

2.1055 ODE No. 1055

Problem in Latex
Mathematica input
Maple input

$(a x + b) y^{'} (x) + y (x) (a1 x^{2} + b1 x + c1) + y^{″} (x) = 0$ ✓ Mathematica : cpu = 0.138796 (sec), leaf count = 421

${{y (x) \to c_{1} \exp (\frac{- b x \sqrt{a^{2} - 4 a1} - \frac{1}{2} a x^{2} \sqrt{a^{2} - 4 a1} - \frac{1}{2} a^{2} x^{2} - a b x + 2 a1 x^{2} + 2 b1 x}{2 \sqrt{a^{2} - 4 a1}}) H_{\frac{- a^{3} + 2 c1 a^{2} - \sqrt{a^{2} - 4 a1} a^{2} + 4 a1 a - 2 b b1 a + 2 a1 b^{2} + 2 {b1}^{2} + 4 \sqrt{a^{2} - 4 a1} a1 - 8 a1 c1}{2 {(a^{2} - 4 a1)}^{3 / 2}}} (\frac{a b - 2 b1}{\sqrt{2} {(a^{2} - 4 a1)}^{3 / 4}} + \frac{\sqrt[4]{a^{2} - 4 a1} x}{\sqrt{2}}) + c_{2} \exp (\frac{- b x \sqrt{a^{2} - 4 a1} - \frac{1}{2} a x^{2} \sqrt{a^{2} - 4 a1} - \frac{1}{2} a^{2} x^{2} - a b x + 2 a1 x^{2} + 2 b1 x}{2 \sqrt{a^{2} - 4 a1}})_{1} F_{1} (- \frac{- a^{3} + 2 c1 a^{2} - \sqrt{a^{2} - 4 a1} a^{2} + 4 a1 a - 2 b b1 a + 2 a1 b^{2} + 2 {b1}^{2} + 4 \sqrt{a^{2} - 4 a1} a1 - 8 a1 c1}{4 {(a^{2} - 4 a1)}^{3 / 2}}; \frac{1}{2}; {(\frac{a b - 2 b1}{\sqrt{2} {(a^{2} - 4 a1)}^{3 / 4}} + \frac{\sqrt[4]{a^{2} - 4 a1} x}{\sqrt{2}})}^{2})}}$ ✓ Maple : cpu = 0.451 (sec), leaf count = 262

${y (x) = (_C 2 (a^{2} x + a b - 4 a 1 x - 2 b 1)_{1} F_{1} (\frac{1}{4} (3 {(a^{2} - 4 a 1)}^{3 / 2} + a^{3} - 2 a^{2} c 1 + (2 b 1 b - 4 a 1) a + (- 2 b^{2} + 8 c 1) a 1 - 2 {b 1}^{2}) {(a^{2} - 4 a 1)}^{- \frac{3}{2}}; \frac{3}{2}; \frac{{(a^{2} x + a b - 4 a 1 x - 2 b 1)}^{2}}{2} {(a^{2} - 4 a 1)}^{- \frac{3}{2}}) +_C 1_{1} F_{1} (\frac{1}{4} ({(a^{2} - 4 a 1)}^{\frac{3}{2}} + a^{3} - 2 a^{2} c 1 + (2 b 1 b - 4 a 1) a + (- 2 b^{2} + 8 c 1) a 1 - 2 {b 1}^{2}) {(a^{2} - 4 a 1)}^{- \frac{3}{2}}; \frac{1}{2}; \frac{{(a^{2} x + a b - 4 a 1 x - 2 b 1)}^{2}}{2} {(a^{2} - 4 a 1)}^{- \frac{3}{2}})) e^{- \frac{x}{4} ((a x + 2 b) {(a^{2} - 4 a 1)}^{\frac{3}{2}} + (a^{2} - 4 a 1) (a^{2} x + 2 a b - 4 a 1 x - 4 b 1)) {(a^{2} - 4 a 1)}^{- \frac{3}{2}}}}$

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